Linear Equations Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope in a linear equation represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the line on the y-axis.

Front

How do you write an equation for a total cost that includes a fixed fee and a variable fee?

Back

The equation can be written as C = fixed fee + (variable fee per unit * number of units).

Front

If a service costs a flat fee plus a charge per mile, how would you express this as a linear equation?

Back

C = flat fee + (charge per mile * miles driven).

Front

What is the total cost for renting a paddle boat for h hours if the cost is $15 deposit plus $2 per hour?

Back

C = 2h + 15.

Front

How do you calculate the total cost for a plumber who charges a flat fee plus an hourly rate?

Back

Total cost = flat fee + (hourly rate * number of hours worked).

Front

If you rent 12 large rafts at $100 each and have $1,600 to spend, how do you find the number of small rafts you can rent?

Back

First, calculate the total cost for large rafts, then subtract from $1,600 and divide by the cost of small rafts.

Front

What does it mean to interpret the y-intercept in a real-world context?

Back

Interpreting the y-intercept means understanding what the initial value represents in the context of the problem.

Front

How do you set up an equation for a T-shirt design company that charges an initial fee plus a cost per shirt?

Back

The equation is y = cost per shirt * number of shirts + initial fee.